Mapping minds not averages: a scalable subject-specific manifold learning framework for neuroimaging data

Eloy Geenjaar; Vince Calhoun

REVIEW 4 major objections 5 minor 45 references

Mapping minds not averages: a scalable subject-specific manifold learning framework for neuroimaging data

T0 review · 4 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Decomposing each subject's spatial layer into shared singular vectors and subject-specific singular values lets a nonlinear autoencoder learn individual brain manifolds that scale to hundreds of subjects and separate schizophrenia…

desk verdict The Decomposed layer is a genuinely useful parameterization, but the simulation evidence as reported is questionable because random rotations are outside the capacity of shared U,V with diagonal S_i. read the letter →

arxiv 2505.00196 v1 pith:QRVJ3HRR submitted 2025-04-30 cs.LG q-bio.NC

Eloy Geenjaar , Vince Calhoun This is my paper · ORCID

classification cs.LGq-bio.NC

keywords subject-specificmanifoldlearningfMRIautoencodersingularvaluedecompositionschizophreniaresting-statesubjectgeneralizationsharedresponsemodel

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish that nonlinear autoencoders trained on fMRI fail to capture individual differences not because of insufficient depth, but because they assume a single group-level spatial map. To fix this, it proposes a subject-specific first/last linear layer decomposed as $W_i = U S_i V^T$, where $U$ and $V$ are shared across subjects and only the diagonal singular values $S_i$ vary per subject, paired with a shared nonlinear network. Across simulated rotated data, two naturalistic movie datasets, and resting-state fMRI from schizophrenia patients and controls, this Decomposed layer matches or beats per-subject linear layers, scales to hundreds of subjects, and generalizes to new subjects by fine-tuning only $S_i$. If correct, the field gains a way to learn individually tailored brain manifolds without temporal alignment or per-subject decoders, making subject-specific modeling feasible on large clinical datasets.

What carries the argument

The load-bearing object is the decomposed subject-specific linear layer $W_i = U S_i V^T$ (Eq. 4), placed as the first layer of the encoder and last layer of the decoder of a shared neural network. $U$ and $V$ are shared across subjects and only the diagonal singular values $S_i$ are subject-specific; this replaces an $N \times L$ per-subject matrix with $L$ per-subject numbers, shrinking the parameter count from $IS \times HS \times NS$ to $IS \times HS + HS^2 + HS \times NS$. That reduction is what makes voxelwise whole-brain training possible, allows new subjects to be added by fine-tuning only their singular values, and keeps the subject-specific weights linear and therefore interpretable.

What would settle it

Simulate a dataset where each subject's spatial map is generated with a subject-specific rotation applied to shared components (differing $U_i$ and $V_i$ rather than just $S_i$), then compare the Decomposed model's held-out reconstruction error to the Subject model's; if the Decomposed model fails to match the Subject model on such data, the shared-$U,V$ assumption is the limiting factor.

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Extended reading notes

Core claim

The central claim is that a decomposed subject-specific spatial map, $W_i = U S_i V^T$ with shared orthonormal $U$ and $V$ and per-subject diagonal $S_i$, is enough to let a shared nonlinear autoencoder represent each individual's spatial variation in fMRI data. The paper demonstrates this on three fronts: the Decomposed model recovers the exact rotation angles of simulated half-moon subjects; it outperforms the Group model and the MRMD-AE baseline in reconstruction and event classification on Sherlock and Forrest Gump, including whole-brain data where per-subject linear layers cannot fit in memory; and on roughly 300 resting-state subjects it scales efficiently, generalizes to unseen subjects (even from a single TR), and learns singular values that separate schizophrenia patients from controls with 79.16% label-free classification accuracy. Spatial maps reconstructed from $S_i$ alone show increased basal ganglia, visual, auditory, and somatosensory activation and decreased insula, inferior frontal gyrus, and angular gyrus activation in patients, matching established schizophrenia findings.

Load-bearing premise

The model assumes that all subjects' spatial maps share the same singular vectors $U$ and $V$, so every individual difference must be a rescaling of shared components; if two brains differ by rotating a spatial component rather than scaling it, the Decomposed layer cannot represent that difference.

Editorial extensions

If this is right

The Decomposed model can be trained directly on whole-brain voxelwise data, where per-subject linear layers are memory-prohibitive, enabling subject-specific manifold learning at population scale.
New subjects can be added to a fitted model by fine-tuning only their singular values, even from a single TR, without retraining the shared network or inducing catastrophic forgetting.
Unsupervised subject-specific weights separate schizophrenia patients from controls with 79.16% accuracy, suggesting the singular values carry diagnostic information without label supervision.
Spatial reconstructions driven only by subject-specific weights localize group differences to basal ganglia, sensory, insular, and frontal regions, offering a candidate pipeline for generating interpretable clinical biomarkers.
Because the decomposition is architecture-agnostic, it can be inserted into other autoencoder, variational autoencoder, or foundation-model objectives without changing the training procedure.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

As an extension, the same $W_i = U S_i V^T$ decomposition could be applied to temporal layers instead of spatial maps, letting a model capture individual differences in dynamics rather than topography; the paper notes this possibility but does not test it.
The compact per-subject singular values $S_i$ are a natural target for harmonization: if scanner or site effects are present in multi-site resting-state data, regressing them out of $S_i$ could enable cleaner cross-site pooling for clinical studies.
The 79.16% label-free classification accuracy suggests $S_i$ may trace a continuous illness-related axis; correlating $S_i$ with symptom severity, medication dose, or illness duration would sharpen the clinical interpretation beyond binary group separation.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The one thing you should know: this paper introduces a parameter-efficient way to fit per-subject spatial maps in nonlinear autoencoders, and that idea is worth taking seriously. The Decomposed layer (W_i = U S_i V^T with shared U,V and subject-specific diagonal S_i) is new, scales to hundreds of subjects, and the naturalistic fMRI experiments show consistent gains over the group baseline and MRMD-AE. The fine-tuning scheme for unseen subjects is also clean and practical.

But there is a soft spot that looks load-bearing. The simulation generates each subject as a random rotation of the half-moons dataset. A rotation matrix in 2D has identical singular values (both 1), so under the shared-U/V decomposition every subject should collapse to the same W_i. The paper reports near-perfect classification and a circle in the learned singular values. That is not a minor discrepancy; it suggests either the implementation deviates from Eq. 4 (e.g., S_i not actually diagonal, or U/V not fully shared) or the result is an artifact. The authors need to explain this explicitly, because the simulation is the primary evidence that the decomposition can capture true subject-specific spatial variation.

The stress-test note about capacity is related: real topographic shifts, shape changes, and component reorientations are not amplitude scalings of a common basis. The paper never quantifies the information lost by the shared U/V assumption, and never compares Decomposed to the full Subject model on data where the latter is trainable. That comparison would directly address the capacity concern.

Other weaknesses are less central but still worth fixing: the 79.16% SVM accuracy on subject weights comes without confidence intervals or a null permutation baseline; the clinical group differences are not controlled for site or motion; and no code is released. The citation pattern looks fine.

Who is this for? Researchers building subject-specific models on unstructured fMRI, especially large resting-state datasets. They would get a useful parameterization and a promising training recipe, but should not trust the clinical spatial maps until the simulation question is resolved.

Recommendation: send this to peer review. The core idea is novel and the naturalistic results are suggestive, but the paper needs major revision—at minimum a clarification of the simulation implementation and a direct capacity check—before the central claims can be accepted.

Referee Report

4 major / 5 minor

Summary. The paper proposes a scalable framework for learning subject-specific nonlinear manifolds from fMRI data. It compares three architectures: a Group model with a shared first linear layer, a Subject model with a separate spatial weight matrix per subject, and a Decomposed model in which each subject-specific weight matrix is parameterized as W_i = U S_i V^T with U and V shared and only the diagonal singular values S_i varying across subjects. On simulated rotated half-moons data and on the Sherlock and Forrest Gump naturalistic fMRI datasets, the Subject and Decomposed models improve held-out reconstruction and label classification over the Group model, and the Decomposed model is the only one that scales to whole-brain voxelwise data. On the fBIRN resting-state schizophrenia dataset, the authors report that a VAE with the Decomposed layer can fine-tune subject weights for unseen subjects with as little as one TR of data, that an SVM on the learned subject weights separates patients from controls with 79.16% accuracy, and that subject-specific spatial reconstructions show group differences in basal ganglia, visual, auditory, somatosensory, insula, inferior frontal gyrus, and angular gyrus regions.

Significance. If the central claims hold, the Decomposed layer is a practically useful contribution: it introduces a parameter-efficient way to give each subject a distinct linear spatial map while retaining a shared nonlinear manifold, and it enables whole-brain analysis and generalization to unseen subjects without retraining the shared network. The simulation result that a Group model cannot separate rotated half-moons despite nonlinear layers is a clean illustration of the need for subject-specific spatial conditioning, and the one-TR fine-tuning result is an appealing practical capability. However, the manuscript currently provides only limited evidence for the key representational assumption behind the Decomposed model, and the main quantitative claims are not supported by inferential statistics or confound analyses. The clinical interpretation of the group-difference maps is therefore premature. With additional capacity checks and statistical rigor, the paper could make a solid contribution to manifold learning for neuroimaging.

major comments (4)

[Section 2.2, Figures 2 and 3] The parameterization W_i = U S_i V^T restricts all subject-specific spatial maps to a single low-dimensional subspace of matrix space: only the diagonal entries of S_i vary across subjects. This cannot express topographic shifts, shape changes, or component reorientations that differ between subjects, and the paper's supporting argument (the qualitative similarity of ICA resting networks in Section 4.2) is not direct evidence that amplitude rescaling of a common basis is sufficient. Because the whole-brain fBIRN results in Figures 4b and 5 are derived entirely from the frozen shared U and V together with subject-specific S_i, this assumption is load-bearing. The manuscript never quantifies the information loss relative to the Subject model in a setting where the Subject model is trainable, nor does it test a simulation with subject-specific spatial variation beyond global scaling. Please add a direct capacity check, for example a comparison of Decomposed versus Subject on the ROI-level data for reconstruction and classification, and a simulation where subjects differ by local translation or reorientation of spatial maps, to determine whether the Decomposed model recovers the true generating factors.
[Section 2.3, Figure 4] The text repeatedly states that the Subject and Decomposed models significantly outperform the Group model, and that the Decomposed model significantly improves whole-brain classification, but the paper reports no p-values, confidence intervals, paired-test details, or multiple-comparison corrections. The bar charts show point estimates without error bars. Since these significance statements are central to the claim that subject-specific spatial maps improve nonlinear manifold learning, please report the exact test procedure, the number of paired observations, and corrections for the multiple ROIs and label types, or provide bootstrap confidence intervals. The comparison with MRMD-AE should also state explicitly which settings and data are matched and whether the MRMD-AE numbers are from the original publication rather than re-evaluated under identical conditions.
[Section 2.4, Figure 5] The 79.16% SVM classification accuracy on subject-specific weights is reported without uncertainty, permutation testing, or description of the cross-validation details beyond '20-fold.' The fBIRN dataset is multi-site, and diagnosis can be correlated with acquisition site; the subject-specific singular values could in principle absorb site, motion, or global-signal differences rather than clinically meaningful spatial variation. Please report fold construction at the subject level, class balance, hyperparameter selection details, a permutation null, and confidence intervals. Please also add a confound analysis, such as testing whether an SVM can classify acquisition site from the same weights, or whether the patient-control separation survives regressing out site and motion parameters. This is important because the subsequent spatial interpretation in Figure 5 rests on the assumption that the weights capture diagnosis-related neurobiology rather than acquisition artifacts.
[Section 2.4, Figure 5] The spatial group-difference analysis uses 64 FastICA sources and two-sided t-tests on the whitened unmixing matrix, with FDR correction for 64 tests, but it does not account for covariates such as age, sex, site, medication, or motion, and the effective dependence among the 64 tests is not discussed. The manuscript should clarify how the subject-specific reconstructions are constructed from S_i and the shared matrices, and what exactly is being compared in the t-test (e.g., source amplitudes, spatial maps, or unmixing coefficients). A permutation test in which diagnosis labels are shuffled, or in which site labels are permuted, would substantially strengthen the claim that the observed regions reflect schizophrenia-related differences rather than amplitude or site effects.

minor comments (5)

[Abstract] The phrase 'To test this, we apply the framework to temporally unstructured resting-state fMRI data ... We further apply our method to a large resting-state fMRI dataset ...' describes the same fBIRN application twice and should be condensed.
[Section 4.1] There are typos: 'approxiation theorem' should be 'approximation theorem,' and 'spatial spatial activation map' should be 'spatial activation map.' In Appendix A, 'the the number' should be corrected, and in Section 4.3.2 'dscribed' should be 'described.'
[Section 2.1] The simulation experiment does not explicitly state what classification label is being predicted. Please clarify that the target is the half-moon cluster label after rotation, and specify how the classification is performed for the Subject and Decomposed models relative to the encoder-decoder formulation used elsewhere.
[Section 4.2, Eqs. (2)-(4)] The dimension conventions are unclear: W_i in Eq. (4) is written as an L x N matrix, while Eq. (2) uses W_enc^i in a way that suggests an N x L map for the encoder. Please define the exact shapes of U, S_i, and V for both the encoder and decoder, and clarify which matrices are transposed in the implementation.
[General] The paper would benefit from a code and data availability statement. Several datasets and label repositories are listed, but no implementation, training hyperparameters, or random seeds are provided in the main text or appendices beyond the simulation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Decomposed model's subject-specific weights are learned unsupervised and evaluated on held-out data, and the central claims do not reduce to their inputs.

full rationale

The derivation chain is self-contained. Equation (4) introduces the shared-U/V decomposition as an explicit modeling assumption ('we assume that these matrices are shared between subjects and that only singular values vary across subjects'), not as a quantity fitted to the outcome being predicted. The per-subject singular values are optimized for unsupervised reconstruction; the naturalistic-movie evaluations classify held-out test timepoints after embedding, and the MRMD-AE comparison uses published external numbers. The schizophrenia analysis is post-hoc: the VAE is trained without diagnostic labels, the RBF SVM is cross-validated on the learned subject weights, and unseen-subject generalization is tested by fine-tuning only the subject-specific weights on a small subset of that subject's data and reconstructing held-out timepoints. The self-citation used to motivate shared spatial structure (Calhoun and Adali 2012) cites an empirical observation about ICA map similarity; it is not an assertion of the paper's target result, and the adequacy of the decomposition is tested through reconstruction, classification, and held-out subject generalization rather than imported by citation. No step, by the paper's own equations, is equivalent by construction to its own input: the subject-specific parameters are not fitted to labels, the reported predictions are not the fitted values renamed, and no uniqueness theorem is imported from the authors' prior work to force the modeling choice.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities. Its key added content is a parameterization (shared U,V with subject-specific S_i) and the analysis pipeline around it. The main axiomatic load is that this parameterization is expressive enough for real subject variability, and that reconstruction error tracks cognitive relevance. The learned parameters (S_i, U, V, network weights) are fitted to data, and several analysis choices (number of ICA sources, FDR threshold) are made by the authors.

free parameters (4)

subject-specific singular values S_i = Learned for each subject during training or fine-tuning
These per-subject scalings are the core of the model's individualization; they are optimized to reconstruct each subject's data and later fine-tuned for unseen subjects.
shared matrices U and V = Learned via backpropagation
The shared spatial bases are trained on the whole population; they define the common manifold structure that the subject-specific scalings modify.
latent dimension d and hidden size L = L=256 for some autoencoder experiments; d not fully specified
Architecture choices that determine model capacity; they are hand-picked and not derived from theory.
number of ICA sources (64) for spatial analysis = 64
Analysis choice in Section 2.4; the number of sources affects the group-difference maps and is selected by the authors.

assumptions (5)

domain assumption Brain activity lies on a low-dimensional non-linear manifold
Standard assumption in neuroimaging, cited in the introduction with refs [5,19,42]; it motivates the autoencoding objective.
ad hoc to paper Subject-specific spatial maps share structure such that W_i = U S_i V^T with shared U,V is sufficient
Core modeling assumption introduced in Section 4.2; justified only by reference to ICA similarity, not proven or tested against alternative parameterizations.
domain assumption Reconstruction quality is a valid proxy for capturing cognitive representations
Used in Section 2.2; assumes that lower MSE on held-out fMRI data implies better manifold learning for cognition.
standard math Multi-layer perceptrons can approximate the relevant fMRI manifold (universal approximation)
Invoked in Section 4.1 to justify using neural networks as flexible maps.
domain assumption Fast ICA sources from model reconstructions correspond to meaningful brain networks
Spatial ICA applied in Section 2.4 assumes linear mixing and independence; the resulting maps are interpreted as brain activations.

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Cite this review

Pith. "Pith review of Mapping minds not averages: a scalable subject-specific manifold learning framework for neuroimaging data." pith.science (2026). https://pith.science/paper/QRVJ3HRR

@misc{pith2026250500196,
  author       = {Pith},
  title        = {Pith review of: Mapping minds not averages: a scalable subject-specific manifold learning framework for neuroimaging data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QRVJ3HRR}},
  note         = {Machine review of arXiv:2505.00196}
}

read the original abstract

Mental and cognitive representations are believed to reside on low-dimensional, non-linear manifolds embedded within high-dimensional brain activity. Uncovering these manifolds is key to understanding individual differences in brain function, yet most existing machine learning methods either rely on population-level spatial alignment or assume data that is temporally structured, either because data is aligned among subjects or because event timings are known. We introduce a manifold learning framework that can capture subject-specific spatial variations across both structured and temporally unstructured neuroimaging data. On simulated data and two naturalistic fMRI datasets (Sherlock and Forrest Gump), our framework outperforms group-based baselines by recovering more accurate and individualized representations. We further show that the framework scales efficiently to large datasets and generalizes well to new subjects. To test this, we apply the framework to temporally unstructured resting-state fMRI data from individuals with schizophrenia and healthy controls. We further apply our method to a large resting-state fMRI dataset comprising individuals with schizophrenia and controls. In this setting, we demonstrate that the framework scales efficiently to large populations and generalizes robustly to unseen subjects. The learned subject-specific spatial maps our model finds reveal clinically relevant patterns, including increased activation in the basal ganglia, visual, auditory, and somatosensory regions, and decreased activation in the insula, inferior frontal gyrus, and angular gyrus. These findings suggest that our framework can uncover clinically relevant subject-specific brain activity patterns. Our approach thus provides a scalable and individualized framework for modeling brain activity, with applications in computational neuroscience and clinical research.

Figures

Figures reproduced from arXiv: 2505.00196 by the authors.

**Figure 1.** Subfigure a: The three main models tested in our framework, subject-specific parameters have different colors across subjects, and parameters shared across subjects are gray. The Group model assumes the same spatial weights and neural network for all subjects in a dataset, and requires the smallest number of parameters. This is currently the most common way neural networks are applied to neuroimaging data. The Subje… view at source ↗

**Figure 2.** The classification results in this figure are calculated with a radial basis function (RBF) support vector machine (SVM) for auto-encoder models that have embedded an unseen 50% of the timeseries. The top row shows performance for the auditory, early visual, posteromedial cortex regions of interest (ROIs), and whole-brain data from the Sherlock dataset [14]. Separate RBF-SVMs are trained for the music presence (bin… view at source ↗

**Figure 3.** Reconstruction improvements in terms of percentage reduction in mean squared error over the Group model on the test set. For both datasets and each region of interest (ROI) or whole-brain data, both the Subject and Decomposed models significantly outperform the Group model in terms of generalization to new fMRI data from the same subjects. This indicates that using subject-specific spatial maps helps the autoencoder… view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Subfigure a: We evaluate reconstruction performance as a function of the percentage of data we fine-tune the subject-specific weights of unseen subjects on. The total number of timesteps is 157, and even with 1% of those timesteps, our model outperforms the group laye…

**Figure 5.** Figure 5: Significantly different brain activations between schizophrenia patients and control subjects as indicated by our Decomposed model. These brain regions are a selection from all the significant regions. We generally find significantly increased basal ganglia, visual, au…

**Figure 6.** Figure 6: Each of these sub-figures indicates a different regime parameter scaling regime. IS is short for input size, and HS is short for hidden size. The number of subjects increase from left to right on the x-axis, and the number of parameters increase logarithmically on the …

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